11 citations · 19 across the 14 of their papers we have counts for
6 papers · 1 filter
Combinatorial Lefschetz theorems beyond positivity
Karim Adiprasito
Consider a simplicial complex that allows for an embedding into . How many faces of dimension or higher can it have? How dense can they be? This basic q…
Semistable reduction in characteristic 0
Karim Adiprasito, Gaku Liu, Michael Temkin
In 2000 Abramovich and Karu proved that any dominant morphism of varieties of characteristic zero can be made weakly semistable by replacing by a smooth alteration…
Log smoothness and polystability over valuation rings
Karim Adiprasito, Gaku Liu, Igor Pak +1
Let be a valuation ring of height one of residual characteristic exponent and with algebraically closed field of fractions. Our main result provides a best possib…
Theorems of Carathéodory, Helly, and Tverberg without dimension
Karim Adiprasito, Imre Bárány, Nabil H. Mustafa +1
We prove a no-dimensional version of Carathédory's theorem: given an -element set , a point $a \in \conv P$, and an integer , , there is a subse…
Rigidity with few locations
Karim Adiprasito, Eran Nevo
Graphs triangulating the -sphere are generically rigid in -space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a \emph{finite} subset in -space so that the ve…
QGLBT for polytopes
Karim Adiprasito, Mikhail Burens, Eran Nevo
We extend the assertion of the Generalized Lower Bound Theorem (GLBT) to general polytopes under the assumption that their low dimensional skeleton is simplicial, with partial resu…